Properties

Label 684.3.b.a.683.19
Level $684$
Weight $3$
Character 684.683
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 683.19
Character \(\chi\) \(=\) 684.683
Dual form 684.3.b.a.683.17

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.45112 + 1.37632i) q^{2} +(0.211495 - 3.99440i) q^{4} -4.00161i q^{5} -12.0281i q^{7} +(5.19067 + 6.08744i) q^{8} +O(q^{10})\) \(q+(-1.45112 + 1.37632i) q^{2} +(0.211495 - 3.99440i) q^{4} -4.00161i q^{5} -12.0281i q^{7} +(5.19067 + 6.08744i) q^{8} +(5.50748 + 5.80681i) q^{10} +15.7569 q^{11} -4.74430i q^{13} +(16.5544 + 17.4542i) q^{14} +(-15.9105 - 1.68959i) q^{16} -7.81502i q^{17} +(13.2190 + 13.6476i) q^{19} +(-15.9840 - 0.846319i) q^{20} +(-22.8651 + 21.6865i) q^{22} +3.71703 q^{23} +8.98715 q^{25} +(6.52966 + 6.88454i) q^{26} +(-48.0450 - 2.54387i) q^{28} +46.8191 q^{29} -56.2449 q^{31} +(25.4135 - 19.4462i) q^{32} +(10.7560 + 11.3405i) q^{34} -48.1316 q^{35} -52.6460i q^{37} +(-37.9658 - 1.61075i) q^{38} +(24.3595 - 20.7710i) q^{40} -31.8316 q^{41} -30.9062i q^{43} +(3.33249 - 62.9393i) q^{44} +(-5.39385 + 5.11582i) q^{46} -35.5329 q^{47} -95.6743 q^{49} +(-13.0414 + 12.3692i) q^{50} +(-18.9506 - 1.00339i) q^{52} +64.9036 q^{53} -63.0527i q^{55} +(73.2201 - 62.4337i) q^{56} +(-67.9401 + 64.4380i) q^{58} +31.1080i q^{59} +6.13439 q^{61} +(81.6180 - 77.4108i) q^{62} +(-10.1139 + 63.1958i) q^{64} -18.9848 q^{65} -102.779 q^{67} +(-31.2163 - 1.65284i) q^{68} +(69.8447 - 66.2444i) q^{70} +89.2964i q^{71} +101.964 q^{73} +(72.4577 + 76.3957i) q^{74} +(57.3099 - 49.9157i) q^{76} -189.524i q^{77} +26.6868 q^{79} +(-6.76108 + 63.6677i) q^{80} +(46.1914 - 43.8104i) q^{82} -62.4230 q^{83} -31.2726 q^{85} +(42.5367 + 44.8485i) q^{86} +(81.7886 + 95.9190i) q^{88} -17.0849 q^{89} -57.0647 q^{91} +(0.786132 - 14.8473i) q^{92} +(51.5625 - 48.9046i) q^{94} +(54.6124 - 52.8973i) q^{95} -134.344i q^{97} +(138.835 - 131.678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 8 q^{4} + O(q^{10}) \) \( 80 q - 8 q^{4} - 56 q^{16} - 400 q^{25} - 464 q^{49} - 272 q^{58} - 352 q^{61} - 200 q^{64} + 480 q^{73} + 152 q^{76} + 32 q^{82} + 704 q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45112 + 1.37632i −0.725560 + 0.688159i
\(3\) 0 0
\(4\) 0.211495 3.99440i 0.0528737 0.998601i
\(5\) 4.00161i 0.800321i −0.916445 0.400161i \(-0.868954\pi\)
0.916445 0.400161i \(-0.131046\pi\)
\(6\) 0 0
\(7\) 12.0281i 1.71829i −0.511728 0.859147i \(-0.670995\pi\)
0.511728 0.859147i \(-0.329005\pi\)
\(8\) 5.19067 + 6.08744i 0.648834 + 0.760930i
\(9\) 0 0
\(10\) 5.50748 + 5.80681i 0.550748 + 0.580681i
\(11\) 15.7569 1.43244 0.716221 0.697874i \(-0.245870\pi\)
0.716221 + 0.697874i \(0.245870\pi\)
\(12\) 0 0
\(13\) 4.74430i 0.364946i −0.983211 0.182473i \(-0.941590\pi\)
0.983211 0.182473i \(-0.0584102\pi\)
\(14\) 16.5544 + 17.4542i 1.18246 + 1.24673i
\(15\) 0 0
\(16\) −15.9105 1.68959i −0.994409 0.105599i
\(17\) 7.81502i 0.459707i −0.973225 0.229853i \(-0.926175\pi\)
0.973225 0.229853i \(-0.0738247\pi\)
\(18\) 0 0
\(19\) 13.2190 + 13.6476i 0.695738 + 0.718296i
\(20\) −15.9840 0.846319i −0.799202 0.0423159i
\(21\) 0 0
\(22\) −22.8651 + 21.6865i −1.03932 + 0.985748i
\(23\) 3.71703 0.161610 0.0808050 0.996730i \(-0.474251\pi\)
0.0808050 + 0.996730i \(0.474251\pi\)
\(24\) 0 0
\(25\) 8.98715 0.359486
\(26\) 6.52966 + 6.88454i 0.251141 + 0.264790i
\(27\) 0 0
\(28\) −48.0450 2.54387i −1.71589 0.0908526i
\(29\) 46.8191 1.61445 0.807226 0.590243i \(-0.200968\pi\)
0.807226 + 0.590243i \(0.200968\pi\)
\(30\) 0 0
\(31\) −56.2449 −1.81435 −0.907175 0.420753i \(-0.861766\pi\)
−0.907175 + 0.420753i \(0.861766\pi\)
\(32\) 25.4135 19.4462i 0.794172 0.607693i
\(33\) 0 0
\(34\) 10.7560 + 11.3405i 0.316352 + 0.333545i
\(35\) −48.1316 −1.37519
\(36\) 0 0
\(37\) 52.6460i 1.42287i −0.702754 0.711433i \(-0.748047\pi\)
0.702754 0.711433i \(-0.251953\pi\)
\(38\) −37.9658 1.61075i −0.999101 0.0423882i
\(39\) 0 0
\(40\) 24.3595 20.7710i 0.608989 0.519275i
\(41\) −31.8316 −0.776380 −0.388190 0.921579i \(-0.626899\pi\)
−0.388190 + 0.921579i \(0.626899\pi\)
\(42\) 0 0
\(43\) 30.9062i 0.718748i −0.933194 0.359374i \(-0.882990\pi\)
0.933194 0.359374i \(-0.117010\pi\)
\(44\) 3.33249 62.9393i 0.0757385 1.43044i
\(45\) 0 0
\(46\) −5.39385 + 5.11582i −0.117258 + 0.111213i
\(47\) −35.5329 −0.756020 −0.378010 0.925802i \(-0.623391\pi\)
−0.378010 + 0.925802i \(0.623391\pi\)
\(48\) 0 0
\(49\) −95.6743 −1.95254
\(50\) −13.0414 + 12.3692i −0.260828 + 0.247384i
\(51\) 0 0
\(52\) −18.9506 1.00339i −0.364435 0.0192960i
\(53\) 64.9036 1.22460 0.612298 0.790627i \(-0.290245\pi\)
0.612298 + 0.790627i \(0.290245\pi\)
\(54\) 0 0
\(55\) 63.0527i 1.14641i
\(56\) 73.2201 62.4337i 1.30750 1.11489i
\(57\) 0 0
\(58\) −67.9401 + 64.4380i −1.17138 + 1.11100i
\(59\) 31.1080i 0.527255i 0.964625 + 0.263627i \(0.0849190\pi\)
−0.964625 + 0.263627i \(0.915081\pi\)
\(60\) 0 0
\(61\) 6.13439 0.100564 0.0502819 0.998735i \(-0.483988\pi\)
0.0502819 + 0.998735i \(0.483988\pi\)
\(62\) 81.6180 77.4108i 1.31642 1.24856i
\(63\) 0 0
\(64\) −10.1139 + 63.1958i −0.158030 + 0.987434i
\(65\) −18.9848 −0.292074
\(66\) 0 0
\(67\) −102.779 −1.53401 −0.767004 0.641642i \(-0.778254\pi\)
−0.767004 + 0.641642i \(0.778254\pi\)
\(68\) −31.2163 1.65284i −0.459064 0.0243064i
\(69\) 0 0
\(70\) 69.8447 66.2444i 0.997781 0.946348i
\(71\) 89.2964i 1.25770i 0.777528 + 0.628848i \(0.216473\pi\)
−0.777528 + 0.628848i \(0.783527\pi\)
\(72\) 0 0
\(73\) 101.964 1.39676 0.698382 0.715725i \(-0.253904\pi\)
0.698382 + 0.715725i \(0.253904\pi\)
\(74\) 72.4577 + 76.3957i 0.979158 + 1.03237i
\(75\) 0 0
\(76\) 57.3099 49.9157i 0.754077 0.656786i
\(77\) 189.524i 2.46136i
\(78\) 0 0
\(79\) 26.6868 0.337808 0.168904 0.985633i \(-0.445977\pi\)
0.168904 + 0.985633i \(0.445977\pi\)
\(80\) −6.76108 + 63.6677i −0.0845135 + 0.795846i
\(81\) 0 0
\(82\) 46.1914 43.8104i 0.563310 0.534273i
\(83\) −62.4230 −0.752084 −0.376042 0.926603i \(-0.622715\pi\)
−0.376042 + 0.926603i \(0.622715\pi\)
\(84\) 0 0
\(85\) −31.2726 −0.367913
\(86\) 42.5367 + 44.8485i 0.494613 + 0.521494i
\(87\) 0 0
\(88\) 81.7886 + 95.9190i 0.929416 + 1.08999i
\(89\) −17.0849 −0.191965 −0.0959826 0.995383i \(-0.530599\pi\)
−0.0959826 + 0.995383i \(0.530599\pi\)
\(90\) 0 0
\(91\) −57.0647 −0.627084
\(92\) 0.786132 14.8473i 0.00854492 0.161384i
\(93\) 0 0
\(94\) 51.5625 48.9046i 0.548537 0.520262i
\(95\) 54.6124 52.8973i 0.574867 0.556814i
\(96\) 0 0
\(97\) 134.344i 1.38499i −0.721423 0.692494i \(-0.756512\pi\)
0.721423 0.692494i \(-0.243488\pi\)
\(98\) 138.835 131.678i 1.41668 1.34366i
\(99\) 0 0
\(100\) 1.90073 35.8983i 0.0190073 0.358983i
\(101\) 113.622i 1.12497i −0.826809 0.562483i \(-0.809846\pi\)
0.826809 0.562483i \(-0.190154\pi\)
\(102\) 0 0
\(103\) 92.7894 0.900868 0.450434 0.892810i \(-0.351269\pi\)
0.450434 + 0.892810i \(0.351269\pi\)
\(104\) 28.8806 24.6261i 0.277698 0.236789i
\(105\) 0 0
\(106\) −94.1829 + 89.3280i −0.888518 + 0.842717i
\(107\) 9.75736i 0.0911903i 0.998960 + 0.0455951i \(0.0145184\pi\)
−0.998960 + 0.0455951i \(0.985482\pi\)
\(108\) 0 0
\(109\) 6.03824i 0.0553967i 0.999616 + 0.0276984i \(0.00881779\pi\)
−0.999616 + 0.0276984i \(0.991182\pi\)
\(110\) 86.7807 + 91.4971i 0.788915 + 0.831791i
\(111\) 0 0
\(112\) −20.3225 + 191.373i −0.181451 + 1.70869i
\(113\) −203.980 −1.80513 −0.902565 0.430554i \(-0.858318\pi\)
−0.902565 + 0.430554i \(0.858318\pi\)
\(114\) 0 0
\(115\) 14.8741i 0.129340i
\(116\) 9.90200 187.014i 0.0853620 1.61219i
\(117\) 0 0
\(118\) −42.8146 45.1415i −0.362835 0.382555i
\(119\) −93.9995 −0.789912
\(120\) 0 0
\(121\) 127.279 1.05189
\(122\) −8.90174 + 8.44288i −0.0729651 + 0.0692039i
\(123\) 0 0
\(124\) −11.8955 + 224.665i −0.0959314 + 1.81181i
\(125\) 136.003i 1.08803i
\(126\) 0 0
\(127\) 112.456 0.885482 0.442741 0.896649i \(-0.354006\pi\)
0.442741 + 0.896649i \(0.354006\pi\)
\(128\) −72.3011 105.625i −0.564852 0.825192i
\(129\) 0 0
\(130\) 27.5492 26.1291i 0.211917 0.200993i
\(131\) 82.4318 0.629250 0.314625 0.949216i \(-0.398121\pi\)
0.314625 + 0.949216i \(0.398121\pi\)
\(132\) 0 0
\(133\) 164.154 158.999i 1.23424 1.19548i
\(134\) 149.144 141.456i 1.11301 1.05564i
\(135\) 0 0
\(136\) 47.5735 40.5652i 0.349805 0.298273i
\(137\) 249.682i 1.82250i 0.411854 + 0.911250i \(0.364881\pi\)
−0.411854 + 0.911250i \(0.635119\pi\)
\(138\) 0 0
\(139\) 3.28561i 0.0236375i −0.999930 0.0118188i \(-0.996238\pi\)
0.999930 0.0118188i \(-0.00376211\pi\)
\(140\) −10.1796 + 192.257i −0.0727113 + 1.37326i
\(141\) 0 0
\(142\) −122.900 129.580i −0.865495 0.912533i
\(143\) 74.7552i 0.522764i
\(144\) 0 0
\(145\) 187.352i 1.29208i
\(146\) −147.962 + 140.335i −1.01344 + 0.961196i
\(147\) 0 0
\(148\) −210.290 11.1344i −1.42088 0.0752322i
\(149\) 40.7940i 0.273785i −0.990586 0.136893i \(-0.956288\pi\)
0.990586 0.136893i \(-0.0437115\pi\)
\(150\) 0 0
\(151\) −240.053 −1.58975 −0.794876 0.606772i \(-0.792464\pi\)
−0.794876 + 0.606772i \(0.792464\pi\)
\(152\) −14.4636 + 151.310i −0.0951551 + 0.995462i
\(153\) 0 0
\(154\) 260.846 + 275.023i 1.69381 + 1.78586i
\(155\) 225.070i 1.45206i
\(156\) 0 0
\(157\) 72.1857 0.459782 0.229891 0.973216i \(-0.426163\pi\)
0.229891 + 0.973216i \(0.426163\pi\)
\(158\) −38.7257 + 36.7295i −0.245100 + 0.232465i
\(159\) 0 0
\(160\) −77.8159 101.695i −0.486350 0.635593i
\(161\) 44.7087i 0.277694i
\(162\) 0 0
\(163\) 98.5895i 0.604844i 0.953174 + 0.302422i \(0.0977951\pi\)
−0.953174 + 0.302422i \(0.902205\pi\)
\(164\) −6.73221 + 127.148i −0.0410501 + 0.775294i
\(165\) 0 0
\(166\) 90.5832 85.9139i 0.545682 0.517553i
\(167\) 53.8093i 0.322211i 0.986937 + 0.161106i \(0.0515060\pi\)
−0.986937 + 0.161106i \(0.948494\pi\)
\(168\) 0 0
\(169\) 146.492 0.866815
\(170\) 45.3803 43.0411i 0.266943 0.253183i
\(171\) 0 0
\(172\) −123.452 6.53649i −0.717742 0.0380029i
\(173\) −66.0323 −0.381690 −0.190845 0.981620i \(-0.561123\pi\)
−0.190845 + 0.981620i \(0.561123\pi\)
\(174\) 0 0
\(175\) 108.098i 0.617703i
\(176\) −250.700 26.6227i −1.42443 0.151265i
\(177\) 0 0
\(178\) 24.7922 23.5143i 0.139282 0.132103i
\(179\) 154.451i 0.862856i 0.902147 + 0.431428i \(0.141990\pi\)
−0.902147 + 0.431428i \(0.858010\pi\)
\(180\) 0 0
\(181\) 36.0989i 0.199441i −0.995015 0.0997206i \(-0.968205\pi\)
0.995015 0.0997206i \(-0.0317949\pi\)
\(182\) 82.8077 78.5392i 0.454987 0.431534i
\(183\) 0 0
\(184\) 19.2939 + 22.6272i 0.104858 + 0.122974i
\(185\) −210.669 −1.13875
\(186\) 0 0
\(187\) 123.140i 0.658503i
\(188\) −7.51503 + 141.933i −0.0399736 + 0.754962i
\(189\) 0 0
\(190\) −6.44559 + 151.924i −0.0339242 + 0.799602i
\(191\) −47.0762 −0.246472 −0.123236 0.992377i \(-0.539327\pi\)
−0.123236 + 0.992377i \(0.539327\pi\)
\(192\) 0 0
\(193\) 45.0791i 0.233570i −0.993157 0.116785i \(-0.962741\pi\)
0.993157 0.116785i \(-0.0372589\pi\)
\(194\) 184.900 + 194.949i 0.953092 + 1.00489i
\(195\) 0 0
\(196\) −20.2346 + 382.162i −0.103238 + 1.94981i
\(197\) 290.498i 1.47461i 0.675560 + 0.737305i \(0.263902\pi\)
−0.675560 + 0.737305i \(0.736098\pi\)
\(198\) 0 0
\(199\) 311.638i 1.56602i −0.622008 0.783011i \(-0.713683\pi\)
0.622008 0.783011i \(-0.286317\pi\)
\(200\) 46.6493 + 54.7087i 0.233247 + 0.273544i
\(201\) 0 0
\(202\) 156.380 + 164.879i 0.774156 + 0.816230i
\(203\) 563.143i 2.77410i
\(204\) 0 0
\(205\) 127.377i 0.621353i
\(206\) −134.648 + 127.708i −0.653633 + 0.619940i
\(207\) 0 0
\(208\) −8.01592 + 75.4843i −0.0385381 + 0.362905i
\(209\) 208.290 + 215.044i 0.996604 + 1.02892i
\(210\) 0 0
\(211\) −274.975 −1.30320 −0.651600 0.758563i \(-0.725902\pi\)
−0.651600 + 0.758563i \(0.725902\pi\)
\(212\) 13.7268 259.251i 0.0647489 1.22288i
\(213\) 0 0
\(214\) −13.4292 14.1591i −0.0627534 0.0661640i
\(215\) −123.674 −0.575229
\(216\) 0 0
\(217\) 676.517i 3.11759i
\(218\) −8.31054 8.76221i −0.0381218 0.0401936i
\(219\) 0 0
\(220\) −251.858 13.3353i −1.14481 0.0606151i
\(221\) −37.0768 −0.167768
\(222\) 0 0
\(223\) −16.0992 −0.0721935 −0.0360968 0.999348i \(-0.511492\pi\)
−0.0360968 + 0.999348i \(0.511492\pi\)
\(224\) −233.900 305.675i −1.04420 1.36462i
\(225\) 0 0
\(226\) 295.999 280.741i 1.30973 1.24222i
\(227\) 259.732i 1.14419i 0.820186 + 0.572096i \(0.193870\pi\)
−0.820186 + 0.572096i \(0.806130\pi\)
\(228\) 0 0
\(229\) −367.921 −1.60664 −0.803322 0.595545i \(-0.796936\pi\)
−0.803322 + 0.595545i \(0.796936\pi\)
\(230\) 20.4715 + 21.5841i 0.0890064 + 0.0938438i
\(231\) 0 0
\(232\) 243.022 + 285.009i 1.04751 + 1.22849i
\(233\) 249.444i 1.07057i −0.844670 0.535287i \(-0.820203\pi\)
0.844670 0.535287i \(-0.179797\pi\)
\(234\) 0 0
\(235\) 142.189i 0.605059i
\(236\) 124.258 + 6.57919i 0.526517 + 0.0278779i
\(237\) 0 0
\(238\) 136.405 129.373i 0.573128 0.543585i
\(239\) 47.0788 0.196982 0.0984912 0.995138i \(-0.468598\pi\)
0.0984912 + 0.995138i \(0.468598\pi\)
\(240\) 0 0
\(241\) 316.682i 1.31403i 0.753877 + 0.657016i \(0.228182\pi\)
−0.753877 + 0.657016i \(0.771818\pi\)
\(242\) −184.696 + 175.176i −0.763208 + 0.723867i
\(243\) 0 0
\(244\) 1.29739 24.5032i 0.00531718 0.100423i
\(245\) 382.851i 1.56266i
\(246\) 0 0
\(247\) 64.7483 62.7149i 0.262139 0.253907i
\(248\) −291.948 342.387i −1.17721 1.38059i
\(249\) 0 0
\(250\) 187.184 + 197.357i 0.748735 + 0.789427i
\(251\) −399.629 −1.59215 −0.796074 0.605199i \(-0.793093\pi\)
−0.796074 + 0.605199i \(0.793093\pi\)
\(252\) 0 0
\(253\) 58.5687 0.231497
\(254\) −163.187 + 154.776i −0.642470 + 0.609353i
\(255\) 0 0
\(256\) 250.291 + 53.7646i 0.977698 + 0.210018i
\(257\) −36.1991 −0.140853 −0.0704263 0.997517i \(-0.522436\pi\)
−0.0704263 + 0.997517i \(0.522436\pi\)
\(258\) 0 0
\(259\) −633.230 −2.44490
\(260\) −4.01519 + 75.8330i −0.0154430 + 0.291665i
\(261\) 0 0
\(262\) −119.618 + 113.452i −0.456559 + 0.433024i
\(263\) 96.8904 0.368405 0.184202 0.982888i \(-0.441030\pi\)
0.184202 + 0.982888i \(0.441030\pi\)
\(264\) 0 0
\(265\) 259.719i 0.980071i
\(266\) −19.3742 + 456.656i −0.0728354 + 1.71675i
\(267\) 0 0
\(268\) −21.7371 + 410.539i −0.0811087 + 1.53186i
\(269\) −193.082 −0.717777 −0.358889 0.933380i \(-0.616844\pi\)
−0.358889 + 0.933380i \(0.616844\pi\)
\(270\) 0 0
\(271\) 388.111i 1.43215i −0.698026 0.716073i \(-0.745938\pi\)
0.698026 0.716073i \(-0.254062\pi\)
\(272\) −13.2042 + 124.341i −0.0485448 + 0.457137i
\(273\) 0 0
\(274\) −343.643 362.319i −1.25417 1.32233i
\(275\) 141.609 0.514943
\(276\) 0 0
\(277\) 152.205 0.549477 0.274738 0.961519i \(-0.411409\pi\)
0.274738 + 0.961519i \(0.411409\pi\)
\(278\) 4.52205 + 4.76782i 0.0162664 + 0.0171504i
\(279\) 0 0
\(280\) −249.835 292.998i −0.892268 1.04642i
\(281\) −25.3220 −0.0901137 −0.0450569 0.998984i \(-0.514347\pi\)
−0.0450569 + 0.998984i \(0.514347\pi\)
\(282\) 0 0
\(283\) 459.492i 1.62365i 0.583903 + 0.811823i \(0.301525\pi\)
−0.583903 + 0.811823i \(0.698475\pi\)
\(284\) 356.686 + 18.8857i 1.25594 + 0.0664990i
\(285\) 0 0
\(286\) 102.887 + 108.479i 0.359745 + 0.379296i
\(287\) 382.872i 1.33405i
\(288\) 0 0
\(289\) 227.925 0.788669
\(290\) 257.855 + 271.870i 0.889157 + 0.937481i
\(291\) 0 0
\(292\) 21.5648 407.284i 0.0738521 1.39481i
\(293\) 122.228 0.417159 0.208579 0.978005i \(-0.433116\pi\)
0.208579 + 0.978005i \(0.433116\pi\)
\(294\) 0 0
\(295\) 124.482 0.421973
\(296\) 320.480 273.268i 1.08270 0.923203i
\(297\) 0 0
\(298\) 56.1456 + 59.1970i 0.188408 + 0.198648i
\(299\) 17.6347i 0.0589789i
\(300\) 0 0
\(301\) −371.741 −1.23502
\(302\) 348.345 330.389i 1.15346 1.09400i
\(303\) 0 0
\(304\) −187.263 239.476i −0.615996 0.787749i
\(305\) 24.5474i 0.0804834i
\(306\) 0 0
\(307\) 515.721 1.67987 0.839937 0.542685i \(-0.182592\pi\)
0.839937 + 0.542685i \(0.182592\pi\)
\(308\) −757.037 40.0834i −2.45791 0.130141i
\(309\) 0 0
\(310\) −309.768 326.603i −0.999251 1.05356i
\(311\) 127.010 0.408393 0.204196 0.978930i \(-0.434542\pi\)
0.204196 + 0.978930i \(0.434542\pi\)
\(312\) 0 0
\(313\) 88.0936 0.281449 0.140725 0.990049i \(-0.455057\pi\)
0.140725 + 0.990049i \(0.455057\pi\)
\(314\) −104.750 + 99.3506i −0.333599 + 0.316403i
\(315\) 0 0
\(316\) 5.64412 106.598i 0.0178611 0.337335i
\(317\) 581.946 1.83579 0.917896 0.396821i \(-0.129887\pi\)
0.917896 + 0.396821i \(0.129887\pi\)
\(318\) 0 0
\(319\) 737.722 2.31261
\(320\) 252.885 + 40.4719i 0.790265 + 0.126475i
\(321\) 0 0
\(322\) 61.5333 + 64.8776i 0.191097 + 0.201483i
\(323\) 106.656 103.307i 0.330206 0.319835i
\(324\) 0 0
\(325\) 42.6377i 0.131193i
\(326\) −135.691 143.065i −0.416229 0.438850i
\(327\) 0 0
\(328\) −165.227 193.773i −0.503741 0.590771i
\(329\) 427.392i 1.29906i
\(330\) 0 0
\(331\) 382.665 1.15609 0.578044 0.816006i \(-0.303816\pi\)
0.578044 + 0.816006i \(0.303816\pi\)
\(332\) −13.2021 + 249.343i −0.0397654 + 0.751032i
\(333\) 0 0
\(334\) −74.0588 78.0837i −0.221733 0.233784i
\(335\) 411.279i 1.22770i
\(336\) 0 0
\(337\) 188.264i 0.558645i −0.960197 0.279323i \(-0.909890\pi\)
0.960197 0.279323i \(-0.0901099\pi\)
\(338\) −212.577 + 201.619i −0.628926 + 0.596506i
\(339\) 0 0
\(340\) −6.61400 + 124.916i −0.0194529 + 0.367399i
\(341\) −886.242 −2.59895
\(342\) 0 0
\(343\) 561.401i 1.63674i
\(344\) 188.139 160.424i 0.546917 0.466348i
\(345\) 0 0
\(346\) 95.8207 90.8815i 0.276939 0.262663i
\(347\) 306.142 0.882253 0.441127 0.897445i \(-0.354579\pi\)
0.441127 + 0.897445i \(0.354579\pi\)
\(348\) 0 0
\(349\) 192.206 0.550734 0.275367 0.961339i \(-0.411201\pi\)
0.275367 + 0.961339i \(0.411201\pi\)
\(350\) 148.777 + 156.863i 0.425078 + 0.448180i
\(351\) 0 0
\(352\) 400.437 306.411i 1.13761 0.870485i
\(353\) 455.473i 1.29029i −0.764060 0.645145i \(-0.776797\pi\)
0.764060 0.645145i \(-0.223203\pi\)
\(354\) 0 0
\(355\) 357.329 1.00656
\(356\) −3.61337 + 68.2440i −0.0101499 + 0.191697i
\(357\) 0 0
\(358\) −212.574 224.127i −0.593782 0.626054i
\(359\) 290.476 0.809125 0.404562 0.914510i \(-0.367424\pi\)
0.404562 + 0.914510i \(0.367424\pi\)
\(360\) 0 0
\(361\) −11.5152 + 360.816i −0.0318980 + 0.999491i
\(362\) 49.6835 + 52.3838i 0.137247 + 0.144707i
\(363\) 0 0
\(364\) −12.0689 + 227.939i −0.0331563 + 0.626207i
\(365\) 408.019i 1.11786i
\(366\) 0 0
\(367\) 380.381i 1.03646i 0.855241 + 0.518230i \(0.173409\pi\)
−0.855241 + 0.518230i \(0.826591\pi\)
\(368\) −59.1399 6.28026i −0.160706 0.0170659i
\(369\) 0 0
\(370\) 305.705 289.947i 0.826231 0.783641i
\(371\) 780.665i 2.10422i
\(372\) 0 0
\(373\) 381.277i 1.02219i −0.859524 0.511095i \(-0.829240\pi\)
0.859524 0.511095i \(-0.170760\pi\)
\(374\) 169.480 + 178.691i 0.453155 + 0.477784i
\(375\) 0 0
\(376\) −184.440 216.305i −0.490531 0.575278i
\(377\) 222.124i 0.589187i
\(378\) 0 0
\(379\) −388.600 −1.02533 −0.512665 0.858589i \(-0.671342\pi\)
−0.512665 + 0.858589i \(0.671342\pi\)
\(380\) −199.743 229.332i −0.525639 0.603504i
\(381\) 0 0
\(382\) 68.3132 64.7918i 0.178830 0.169612i
\(383\) 147.201i 0.384337i −0.981362 0.192168i \(-0.938448\pi\)
0.981362 0.192168i \(-0.0615520\pi\)
\(384\) 0 0
\(385\) −758.402 −1.96988
\(386\) 62.0432 + 65.4151i 0.160734 + 0.169469i
\(387\) 0 0
\(388\) −536.624 28.4130i −1.38305 0.0732295i
\(389\) 105.479i 0.271153i 0.990767 + 0.135577i \(0.0432887\pi\)
−0.990767 + 0.135577i \(0.956711\pi\)
\(390\) 0 0
\(391\) 29.0486i 0.0742932i
\(392\) −496.614 582.412i −1.26687 1.48574i
\(393\) 0 0
\(394\) −399.818 421.548i −1.01477 1.06992i
\(395\) 106.790i 0.270355i
\(396\) 0 0
\(397\) −218.614 −0.550665 −0.275332 0.961349i \(-0.588788\pi\)
−0.275332 + 0.961349i \(0.588788\pi\)
\(398\) 428.914 + 452.225i 1.07767 + 1.13624i
\(399\) 0 0
\(400\) −142.990 15.1846i −0.357476 0.0379615i
\(401\) 479.946 1.19687 0.598437 0.801170i \(-0.295789\pi\)
0.598437 + 0.801170i \(0.295789\pi\)
\(402\) 0 0
\(403\) 266.842i 0.662139i
\(404\) −453.851 24.0304i −1.12339 0.0594811i
\(405\) 0 0
\(406\) 775.064 + 817.188i 1.90903 + 2.01278i
\(407\) 829.536i 2.03817i
\(408\) 0 0
\(409\) 138.535i 0.338716i 0.985555 + 0.169358i \(0.0541694\pi\)
−0.985555 + 0.169358i \(0.945831\pi\)
\(410\) −175.312 184.840i −0.427590 0.450829i
\(411\) 0 0
\(412\) 19.6245 370.638i 0.0476322 0.899607i
\(413\) 374.169 0.905979
\(414\) 0 0
\(415\) 249.792i 0.601909i
\(416\) −92.2584 120.569i −0.221775 0.289830i
\(417\) 0 0
\(418\) −598.222 25.3804i −1.43115 0.0607186i
\(419\) −67.4631 −0.161010 −0.0805049 0.996754i \(-0.525653\pi\)
−0.0805049 + 0.996754i \(0.525653\pi\)
\(420\) 0 0
\(421\) 86.5279i 0.205529i 0.994706 + 0.102765i \(0.0327689\pi\)
−0.994706 + 0.102765i \(0.967231\pi\)
\(422\) 399.022 378.453i 0.945549 0.896809i
\(423\) 0 0
\(424\) 336.893 + 395.097i 0.794559 + 0.931833i
\(425\) 70.2347i 0.165258i
\(426\) 0 0
\(427\) 73.7849i 0.172798i
\(428\) 38.9748 + 2.06363i 0.0910627 + 0.00482157i
\(429\) 0 0
\(430\) 179.466 170.215i 0.417363 0.395849i
\(431\) 223.844i 0.519359i −0.965695 0.259680i \(-0.916383\pi\)
0.965695 0.259680i \(-0.0836169\pi\)
\(432\) 0 0
\(433\) 659.844i 1.52389i −0.647642 0.761945i \(-0.724245\pi\)
0.647642 0.761945i \(-0.275755\pi\)
\(434\) −931.102 981.706i −2.14540 2.26200i
\(435\) 0 0
\(436\) 24.1192 + 1.27706i 0.0553192 + 0.00292903i
\(437\) 49.1355 + 50.7286i 0.112438 + 0.116084i
\(438\) 0 0
\(439\) 206.969 0.471455 0.235728 0.971819i \(-0.424253\pi\)
0.235728 + 0.971819i \(0.424253\pi\)
\(440\) 383.830 327.286i 0.872341 0.743832i
\(441\) 0 0
\(442\) 53.8028 51.0294i 0.121726 0.115451i
\(443\) −384.066 −0.866966 −0.433483 0.901162i \(-0.642716\pi\)
−0.433483 + 0.901162i \(0.642716\pi\)
\(444\) 0 0
\(445\) 68.3671i 0.153634i
\(446\) 23.3618 22.1576i 0.0523807 0.0496807i
\(447\) 0 0
\(448\) 760.123 + 121.651i 1.69670 + 0.271542i
\(449\) 345.980 0.770558 0.385279 0.922800i \(-0.374105\pi\)
0.385279 + 0.922800i \(0.374105\pi\)
\(450\) 0 0
\(451\) −501.565 −1.11212
\(452\) −43.1406 + 814.777i −0.0954439 + 1.80260i
\(453\) 0 0
\(454\) −357.474 376.902i −0.787387 0.830180i
\(455\) 228.350i 0.501869i
\(456\) 0 0
\(457\) 268.260 0.587003 0.293502 0.955959i \(-0.405179\pi\)
0.293502 + 0.955959i \(0.405179\pi\)
\(458\) 533.898 506.377i 1.16572 1.10563i
\(459\) 0 0
\(460\) −59.4131 3.14579i −0.129159 0.00683868i
\(461\) 548.763i 1.19037i 0.803587 + 0.595187i \(0.202922\pi\)
−0.803587 + 0.595187i \(0.797078\pi\)
\(462\) 0 0
\(463\) 226.387i 0.488957i 0.969655 + 0.244478i \(0.0786167\pi\)
−0.969655 + 0.244478i \(0.921383\pi\)
\(464\) −744.917 79.1052i −1.60542 0.170485i
\(465\) 0 0
\(466\) 343.314 + 361.973i 0.736725 + 0.776765i
\(467\) 230.126 0.492774 0.246387 0.969171i \(-0.420757\pi\)
0.246387 + 0.969171i \(0.420757\pi\)
\(468\) 0 0
\(469\) 1236.23i 2.63588i
\(470\) −195.697 206.333i −0.416377 0.439006i
\(471\) 0 0
\(472\) −189.368 + 161.472i −0.401204 + 0.342101i
\(473\) 486.984i 1.02956i
\(474\) 0 0
\(475\) 118.801 + 122.653i 0.250108 + 0.258217i
\(476\) −19.8804 + 375.472i −0.0417656 + 0.788807i
\(477\) 0 0
\(478\) −68.3169 + 64.7954i −0.142922 + 0.135555i
\(479\) 496.609 1.03676 0.518381 0.855150i \(-0.326535\pi\)
0.518381 + 0.855150i \(0.326535\pi\)
\(480\) 0 0
\(481\) −249.768 −0.519269
\(482\) −435.855 459.543i −0.904263 0.953409i
\(483\) 0 0
\(484\) 26.9188 508.402i 0.0556173 1.05042i
\(485\) −537.591 −1.10844
\(486\) 0 0
\(487\) −14.9943 −0.0307892 −0.0153946 0.999881i \(-0.504900\pi\)
−0.0153946 + 0.999881i \(0.504900\pi\)
\(488\) 31.8416 + 37.3428i 0.0652492 + 0.0765221i
\(489\) 0 0
\(490\) −526.925 555.562i −1.07536 1.13380i
\(491\) −319.685 −0.651090 −0.325545 0.945526i \(-0.605548\pi\)
−0.325545 + 0.945526i \(0.605548\pi\)
\(492\) 0 0
\(493\) 365.892i 0.742175i
\(494\) −7.64188 + 180.121i −0.0154694 + 0.364618i
\(495\) 0 0
\(496\) 894.886 + 95.0308i 1.80421 + 0.191594i
\(497\) 1074.06 2.16109
\(498\) 0 0
\(499\) 488.538i 0.979033i 0.871994 + 0.489517i \(0.162827\pi\)
−0.871994 + 0.489517i \(0.837173\pi\)
\(500\) −543.252 28.7640i −1.08650 0.0575279i
\(501\) 0 0
\(502\) 579.910 550.017i 1.15520 1.09565i
\(503\) 887.019 1.76346 0.881729 0.471757i \(-0.156380\pi\)
0.881729 + 0.471757i \(0.156380\pi\)
\(504\) 0 0
\(505\) −454.669 −0.900335
\(506\) −84.9902 + 80.6092i −0.167965 + 0.159307i
\(507\) 0 0
\(508\) 23.7839 449.196i 0.0468187 0.884244i
\(509\) 908.075 1.78404 0.892018 0.451999i \(-0.149289\pi\)
0.892018 + 0.451999i \(0.149289\pi\)
\(510\) 0 0
\(511\) 1226.43i 2.40005i
\(512\) −437.199 + 266.461i −0.853904 + 0.520431i
\(513\) 0 0
\(514\) 52.5293 49.8215i 0.102197 0.0969291i
\(515\) 371.306i 0.720983i
\(516\) 0 0
\(517\) −559.887 −1.08295
\(518\) 918.892 871.526i 1.77392 1.68248i
\(519\) 0 0
\(520\) −98.5438 115.569i −0.189507 0.222248i
\(521\) 481.619 0.924413 0.462207 0.886772i \(-0.347058\pi\)
0.462207 + 0.886772i \(0.347058\pi\)
\(522\) 0 0
\(523\) 31.0148 0.0593017 0.0296509 0.999560i \(-0.490560\pi\)
0.0296509 + 0.999560i \(0.490560\pi\)
\(524\) 17.4339 329.266i 0.0332708 0.628370i
\(525\) 0 0
\(526\) −140.600 + 133.352i −0.267299 + 0.253521i
\(527\) 439.555i 0.834069i
\(528\) 0 0
\(529\) −515.184 −0.973882
\(530\) 357.456 + 376.883i 0.674445 + 0.711100i
\(531\) 0 0
\(532\) −600.389 689.327i −1.12855 1.29573i
\(533\) 151.018i 0.283336i
\(534\) 0 0
\(535\) 39.0451 0.0729815
\(536\) −533.490 625.659i −0.995316 1.16727i
\(537\) 0 0
\(538\) 280.185 265.743i 0.520790 0.493945i
\(539\) −1507.53 −2.79689
\(540\) 0 0
\(541\) 437.142 0.808025 0.404013 0.914753i \(-0.367615\pi\)
0.404013 + 0.914753i \(0.367615\pi\)
\(542\) 534.165 + 563.196i 0.985544 + 1.03911i
\(543\) 0 0
\(544\) −151.972 198.607i −0.279361 0.365086i
\(545\) 24.1627 0.0443352
\(546\) 0 0
\(547\) 413.515 0.755968 0.377984 0.925812i \(-0.376617\pi\)
0.377984 + 0.925812i \(0.376617\pi\)
\(548\) 997.333 + 52.8065i 1.81995 + 0.0963623i
\(549\) 0 0
\(550\) −205.492 + 194.899i −0.373622 + 0.354363i
\(551\) 618.902 + 638.969i 1.12323 + 1.15965i
\(552\) 0 0
\(553\) 320.991i 0.580453i
\(554\) −220.868 + 209.483i −0.398678 + 0.378128i
\(555\) 0 0
\(556\) −13.1241 0.694890i −0.0236044 0.00124980i
\(557\) 363.687i 0.652939i 0.945208 + 0.326469i \(0.105859\pi\)
−0.945208 + 0.326469i \(0.894141\pi\)
\(558\) 0 0
\(559\) −146.628 −0.262304
\(560\) 765.799 + 81.3227i 1.36750 + 0.145219i
\(561\) 0 0
\(562\) 36.7452 34.8511i 0.0653829 0.0620126i
\(563\) 35.5312i 0.0631105i −0.999502 0.0315552i \(-0.989954\pi\)
0.999502 0.0315552i \(-0.0100460\pi\)
\(564\) 0 0
\(565\) 816.246i 1.44468i
\(566\) −632.407 666.778i −1.11733 1.17805i
\(567\) 0 0
\(568\) −543.587 + 463.508i −0.957019 + 0.816035i
\(569\) −162.235 −0.285123 −0.142561 0.989786i \(-0.545534\pi\)
−0.142561 + 0.989786i \(0.545534\pi\)
\(570\) 0 0
\(571\) 585.417i 1.02525i −0.858613 0.512625i \(-0.828673\pi\)
0.858613 0.512625i \(-0.171327\pi\)
\(572\) −298.602 15.8103i −0.522032 0.0276404i
\(573\) 0 0
\(574\) −526.954 555.593i −0.918038 0.967932i
\(575\) 33.4055 0.0580965
\(576\) 0 0
\(577\) −333.812 −0.578530 −0.289265 0.957249i \(-0.593411\pi\)
−0.289265 + 0.957249i \(0.593411\pi\)
\(578\) −330.747 + 313.698i −0.572227 + 0.542730i
\(579\) 0 0
\(580\) −748.358 39.6239i −1.29027 0.0683170i
\(581\) 750.827i 1.29230i
\(582\) 0 0
\(583\) 1022.68 1.75416
\(584\) 529.260 + 620.698i 0.906267 + 1.06284i
\(585\) 0 0
\(586\) −177.367 + 168.224i −0.302674 + 0.287072i
\(587\) 691.627 1.17824 0.589120 0.808046i \(-0.299475\pi\)
0.589120 + 0.808046i \(0.299475\pi\)
\(588\) 0 0
\(589\) −743.502 767.609i −1.26231 1.30324i
\(590\) −180.638 + 171.327i −0.306167 + 0.290385i
\(591\) 0 0
\(592\) −88.9503 + 837.627i −0.150254 + 1.41491i
\(593\) 665.716i 1.12262i −0.827604 0.561312i \(-0.810297\pi\)
0.827604 0.561312i \(-0.189703\pi\)
\(594\) 0 0
\(595\) 376.149i 0.632183i
\(596\) −162.948 8.62772i −0.273402 0.0144760i
\(597\) 0 0
\(598\) 24.2709 + 25.5900i 0.0405869 + 0.0427927i
\(599\) 384.914i 0.642595i 0.946978 + 0.321297i \(0.104119\pi\)
−0.946978 + 0.321297i \(0.895881\pi\)
\(600\) 0 0
\(601\) 50.3020i 0.0836972i 0.999124 + 0.0418486i \(0.0133247\pi\)
−0.999124 + 0.0418486i \(0.986675\pi\)
\(602\) 539.441 511.634i 0.896081 0.849891i
\(603\) 0 0
\(604\) −50.7699 + 958.867i −0.0840561 + 1.58753i
\(605\) 509.319i 0.841849i
\(606\) 0 0
\(607\) −481.565 −0.793353 −0.396677 0.917958i \(-0.629837\pi\)
−0.396677 + 0.917958i \(0.629837\pi\)
\(608\) 601.336 + 89.7747i 0.989039 + 0.147656i
\(609\) 0 0
\(610\) 33.7851 + 35.6212i 0.0553854 + 0.0583955i
\(611\) 168.579i 0.275906i
\(612\) 0 0
\(613\) 736.995 1.20228 0.601138 0.799146i \(-0.294714\pi\)
0.601138 + 0.799146i \(0.294714\pi\)
\(614\) −748.373 + 709.796i −1.21885 + 1.15602i
\(615\) 0 0
\(616\) 1153.72 983.759i 1.87292 1.59701i
\(617\) 1144.65i 1.85518i 0.373594 + 0.927592i \(0.378125\pi\)
−0.373594 + 0.927592i \(0.621875\pi\)
\(618\) 0 0
\(619\) 95.5720i 0.154397i 0.997016 + 0.0771987i \(0.0245976\pi\)
−0.997016 + 0.0771987i \(0.975402\pi\)
\(620\) 899.020 + 47.6011i 1.45003 + 0.0767759i
\(621\) 0 0
\(622\) −184.307 + 174.806i −0.296313 + 0.281039i
\(623\) 205.498i 0.329853i
\(624\) 0 0
\(625\) −319.552 −0.511284
\(626\) −127.834 + 121.245i −0.204208 + 0.193682i
\(627\) 0 0
\(628\) 15.2669 288.339i 0.0243104 0.459139i
\(629\) −411.430 −0.654101
\(630\) 0 0
\(631\) 1050.08i 1.66414i 0.554667 + 0.832072i \(0.312846\pi\)
−0.554667 + 0.832072i \(0.687154\pi\)
\(632\) 138.522 + 162.454i 0.219181 + 0.257048i
\(633\) 0 0
\(634\) −844.473 + 800.943i −1.33198 + 1.26332i
\(635\) 450.006i 0.708670i
\(636\) 0 0
\(637\) 453.907i 0.712570i
\(638\) −1070.52 + 1015.34i −1.67794 + 1.59144i
\(639\) 0 0
\(640\) −422.668 + 289.320i −0.660419 + 0.452063i
\(641\) −7.10871 −0.0110900 −0.00554502 0.999985i \(-0.501765\pi\)
−0.00554502 + 0.999985i \(0.501765\pi\)
\(642\) 0 0
\(643\) 65.3645i 0.101655i −0.998707 0.0508277i \(-0.983814\pi\)
0.998707 0.0508277i \(-0.0161859\pi\)
\(644\) −178.584 9.45565i −0.277305 0.0146827i
\(645\) 0 0
\(646\) −12.5881 + 296.704i −0.0194861 + 0.459294i
\(647\) −43.8513 −0.0677764 −0.0338882 0.999426i \(-0.510789\pi\)
−0.0338882 + 0.999426i \(0.510789\pi\)
\(648\) 0 0
\(649\) 490.165i 0.755262i
\(650\) 58.6830 + 61.8724i 0.0902816 + 0.0951882i
\(651\) 0 0
\(652\) 393.807 + 20.8512i 0.603998 + 0.0319803i
\(653\) 143.120i 0.219173i 0.993977 + 0.109587i \(0.0349527\pi\)
−0.993977 + 0.109587i \(0.965047\pi\)
\(654\) 0 0
\(655\) 329.860i 0.503602i
\(656\) 506.457 + 53.7823i 0.772039 + 0.0819853i
\(657\) 0 0
\(658\) −588.228 620.197i −0.893963 0.942549i
\(659\) 461.885i 0.700888i −0.936584 0.350444i \(-0.886031\pi\)
0.936584 0.350444i \(-0.113969\pi\)
\(660\) 0 0
\(661\) 4.75146i 0.00718830i −0.999994 0.00359415i \(-0.998856\pi\)
0.999994 0.00359415i \(-0.00114406\pi\)
\(662\) −555.293 + 526.669i −0.838811 + 0.795573i
\(663\) 0 0
\(664\) −324.017 379.996i −0.487977 0.572283i
\(665\) −636.252 656.881i −0.956770 0.987792i
\(666\) 0 0
\(667\) 174.028 0.260911
\(668\) 214.936 + 11.3804i 0.321761 + 0.0170365i
\(669\) 0 0
\(670\) −566.051 596.815i −0.844853 0.890769i
\(671\) 96.6588 0.144052
\(672\) 0 0
\(673\) 98.2320i 0.145961i −0.997333 0.0729807i \(-0.976749\pi\)
0.997333 0.0729807i \(-0.0232511\pi\)
\(674\) 259.111 + 273.193i 0.384437 + 0.405331i
\(675\) 0 0
\(676\) 30.9822 585.147i 0.0458317 0.865602i
\(677\) −794.006 −1.17283 −0.586415 0.810011i \(-0.699461\pi\)
−0.586415 + 0.810011i \(0.699461\pi\)
\(678\) 0 0
\(679\) −1615.90 −2.37982
\(680\) −162.326 190.370i −0.238715 0.279956i
\(681\) 0 0
\(682\) 1286.04 1219.75i 1.88569 1.78849i
\(683\) 1074.63i 1.57340i −0.617333 0.786702i \(-0.711787\pi\)
0.617333 0.786702i \(-0.288213\pi\)
\(684\) 0 0
\(685\) 999.131 1.45859
\(686\) −772.667 814.660i −1.12634 1.18755i
\(687\) 0 0
\(688\) −52.2188 + 491.734i −0.0758994 + 0.714729i
\(689\) 307.922i 0.446911i
\(690\) 0 0
\(691\) 880.983i 1.27494i 0.770475 + 0.637470i \(0.220019\pi\)
−0.770475 + 0.637470i \(0.779981\pi\)
\(692\) −13.9655 + 263.760i −0.0201813 + 0.381156i
\(693\) 0 0
\(694\) −444.248 + 421.349i −0.640127 + 0.607131i
\(695\) −13.1477 −0.0189176
\(696\) 0 0
\(697\) 248.764i 0.356907i
\(698\) −278.914 + 264.537i −0.399590 + 0.378993i
\(699\) 0 0
\(700\) −431.787 22.8622i −0.616839 0.0326602i
\(701\) 1176.49i 1.67831i −0.543893 0.839154i \(-0.683050\pi\)
0.543893 0.839154i \(-0.316950\pi\)
\(702\) 0 0
\(703\) 718.493 695.929i 1.02204 0.989941i
\(704\) −159.363 + 995.767i −0.226369 + 1.41444i
\(705\) 0 0
\(706\) 626.875 + 660.945i 0.887926 + 0.936183i
\(707\) −1366.65 −1.93302
\(708\) 0 0
\(709\) 694.414 0.979427 0.489714 0.871883i \(-0.337101\pi\)
0.489714 + 0.871883i \(0.337101\pi\)
\(710\) −518.527 + 491.799i −0.730320 + 0.692674i
\(711\) 0 0
\(712\) −88.6821 104.003i −0.124553 0.146072i
\(713\) −209.064 −0.293217
\(714\) 0 0
\(715\) −299.141 −0.418379
\(716\) 616.941 + 32.6656i 0.861649 + 0.0456224i
\(717\) 0 0
\(718\) −421.515 + 399.787i −0.587068 + 0.556807i
\(719\) −268.127 −0.372917 −0.186458 0.982463i \(-0.559701\pi\)
−0.186458 + 0.982463i \(0.559701\pi\)
\(720\) 0 0
\(721\) 1116.08i 1.54796i
\(722\) −479.888 539.436i −0.664665 0.747141i
\(723\) 0 0
\(724\) −144.193 7.63472i −0.199162 0.0105452i
\(725\) 420.770 0.580373
\(726\) 0 0
\(727\) 509.724i 0.701134i −0.936538 0.350567i \(-0.885989\pi\)
0.936538 0.350567i \(-0.114011\pi\)
\(728\) −296.204 347.378i −0.406873 0.477167i
\(729\) 0 0
\(730\) 561.564 + 592.084i 0.769265 + 0.811074i
\(731\) −241.532 −0.330413
\(732\) 0 0
\(733\) −186.307 −0.254170 −0.127085 0.991892i \(-0.540562\pi\)
−0.127085 + 0.991892i \(0.540562\pi\)
\(734\) −523.525 551.978i −0.713250 0.752014i
\(735\) 0 0
\(736\) 94.4627 72.2820i 0.128346 0.0982092i
\(737\) −1619.47 −2.19738
\(738\) 0 0
\(739\) 225.185i 0.304715i −0.988325 0.152358i \(-0.951313\pi\)
0.988325 0.152358i \(-0.0486866\pi\)
\(740\) −44.5553 + 841.496i −0.0602099 + 1.13716i
\(741\) 0 0
\(742\) 1074.44 + 1132.84i 1.44804 + 1.52674i
\(743\) 182.940i 0.246218i 0.992393 + 0.123109i \(0.0392865\pi\)
−0.992393 + 0.123109i \(0.960713\pi\)
\(744\) 0 0
\(745\) −163.242 −0.219116
\(746\) 524.759 + 553.279i 0.703430 + 0.741660i
\(747\) 0 0
\(748\) −491.872 26.0435i −0.657582 0.0348175i
\(749\) 117.362 0.156692
\(750\) 0 0
\(751\) 1130.62 1.50549 0.752746 0.658311i \(-0.228729\pi\)
0.752746 + 0.658311i \(0.228729\pi\)
\(752\) 565.348 + 60.0361i 0.751793 + 0.0798353i
\(753\) 0 0
\(754\) 305.713 + 322.328i 0.405455 + 0.427491i
\(755\) 960.596i 1.27231i
\(756\) 0 0
\(757\) 714.219 0.943486 0.471743 0.881736i \(-0.343625\pi\)
0.471743 + 0.881736i \(0.343625\pi\)
\(758\) 563.905 534.837i 0.743937 0.705590i
\(759\) 0 0
\(760\) 605.484 + 57.8775i 0.796690 + 0.0761546i
\(761\) 1081.23i 1.42080i 0.703799 + 0.710399i \(0.251486\pi\)
−0.703799 + 0.710399i \(0.748514\pi\)
\(762\) 0 0
\(763\) 72.6284 0.0951879
\(764\) −9.95637 + 188.041i −0.0130319 + 0.246127i
\(765\) 0 0
\(766\) 202.596 + 213.606i 0.264485 + 0.278859i
\(767\) 147.586 0.192419
\(768\) 0 0
\(769\) 204.176 0.265508 0.132754 0.991149i \(-0.457618\pi\)
0.132754 + 0.991149i \(0.457618\pi\)
\(770\) 1100.53 1043.80i 1.42926 1.35559i
\(771\) 0 0
\(772\) −180.064 9.53399i −0.233244 0.0123497i
\(773\) −278.794 −0.360665 −0.180333 0.983606i \(-0.557717\pi\)
−0.180333 + 0.983606i \(0.557717\pi\)
\(774\) 0 0
\(775\) −505.481 −0.652233
\(776\) 817.811 697.335i 1.05388 0.898627i
\(777\) 0 0
\(778\) −145.172 153.062i −0.186596 0.196738i
\(779\) −420.782 434.425i −0.540157 0.557670i
\(780\) 0 0
\(781\) 1407.03i 1.80158i
\(782\) 39.9802 + 42.1531i 0.0511256 + 0.0539042i
\(783\) 0 0
\(784\) 1522.23 + 161.650i 1.94162 + 0.206187i
\(785\) 288.859i 0.367973i
\(786\) 0 0
\(787\) −525.124 −0.667247 −0.333624 0.942706i \(-0.608271\pi\)
−0.333624 + 0.942706i \(0.608271\pi\)
\(788\) 1160.37 + 61.4389i 1.47255 + 0.0779681i
\(789\) 0 0
\(790\) 146.977 + 154.965i 0.186047 + 0.196158i
\(791\) 2453.48i 3.10174i
\(792\) 0 0
\(793\) 29.1034i 0.0367003i
\(794\) 317.235 300.882i 0.399540 0.378945i <